Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed
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Revision as of 13:19, 8 August 2014 by PoojaMoolya (Talk | contribs)
| Time | Narration |
| 00:01 | Hello,Welcome to this tutorial on Theorems on Chords and Arcs in Geogebra |
| 00:08 | At the end of this tutorial, |
| 00:09 | you will be able to verify theorems on |
| 00:14 | Chords of circle. |
| 00:16 | Arcs of circle. |
| 00:18 | We assume that you have the basic working knowledge of Geogebra. |
| 00:23 | If not, For relevant tutorials, please visit our website: http://spoken-tutorial.org |
| 00:30 | To record this tutorial I am using |
| 00:32 | Ubuntu Linux OS Version 11.10 |
| 00:36 | Geogebra Version 3.2.47.0 |
| 00:42 | We will use the following Geogebra tools |
| 00:47 | * Circle with Center and Radius |
| 00:49 | * Circular Sector with Center between Two Points |
| 00:53 | * Circular Arc with Center between Two points |
| 00:56 | * Midpoint and |
| 00:58 | Perpendicular line |
| 01:00 | Let's open a new GeoGebra window. |
| 01:02 | Click on Dash home, Media Apps. |
| 01:06 | Under Type Choose Education and GeoGebra. |
| 01:15 | Let's state a theorem |
| 01:17 | Perpendicular from center of circle to a chord bisects the chord |
| 01:23 | Perpendicular from the center A of a circle to chord BC bisects it |
| 01:32 | Let's verify a theorem. |
| 01:37 | For this tutorial I will use 'Grid layout' instead of Axes |
| 01:42 | Right Click on the drawing pad |
| 01:44 | In the 'Graphic view' uncheck 'Axes' |
| 01:47 | Select 'Grid' |
| 01:51 | Let's draw a circle. |
| 01:54 | Select the "Circle with Center and Radius" tool from tool bar. |
| 01:58 | Mark a point 'A' on the drawing pad. |
| 02:01 | A dialogue box opens |
| 02:03 | Let's type value '3' for radius |
| 02:06 | Click OK. |
| 02:07 | A Circle with center 'A' and radius '3cm' is drawn |
| 02:13 | Let's Move the point 'A' and see the movement of the circle. |
| 02:19 | Select “Segment between two points” tool. |
| 02:22 | Mark points 'B' and 'C' on the circumference of the circle |
| 02:27 | A chord 'BC' is drawn. |
| 02:30 | Let's draw a perpendicular line to Chord 'BC' which passes through point 'A'. |
| 02:35 | Click on "Perpendicular line" tool from tool bar |
| 02:39 | Click on the chord 'BC', and point 'A'. |
| 02:44 | Let's Move the point 'B', and see how the perpendicular line moves along with point 'B'. |
| 02:52 | Perpendicular line and Chord 'BC' intersect at a point |
| 02:56 | Click on “Intersect Two objects” tool, |
| 02:58 | Mark the point of intersection as 'D'. |
| 03:03 | Let's verify whether D is the mid point of chord BC |
| 03:08 | Click on the "Distance" tool. |
| 03:11 | Click on the points ,'B' 'D' ...'D' 'C' ... |
| 03:19 | Notice that distances 'BD' and 'DC' are equal. |
| 03:24 | It implies 'D' is midpoint of chord 'BC' |
| 03:29 | Let's measure the angle 'CDA' |
| 03:33 | Click on Angle tool ... |
| 03:35 | Click on the points 'C','D', 'A' |
| 03:42 | angle 'CDA' is '90 degrees |
| 03:46 | TheTheorem is verified. |
| 03:50 | Let's Move the point 'C' and see how the distances move along with point 'C'
|
| 04:03 | Let us save the file now |
| 04:05 | Click on “File”>> "Save As" |
| 04:08 | I will type the file name as "circle-chord" |
| 04:12 | circle-chord |
| 04:16 | Click on Save |
| 04:21 | Let us move on to the next theorem. |
| 04:28 | Inscribed angles subtended by the same arc are equal. |
| 04:34 | Inscribed angles BDC and BEC subtended by the same arc BC are equal |
| 04:44 | Let's verify the theorem. |
| 04:48 | Let'sOpen a new Geogebra window, |
| 04:51 | Click on “File” >> "New" |
| 04:55 | Let's draw a circle |
| 04:57 | Click on "' the Circle with Center through Point tool from toolbar |
| 05:01 | Mark a point A' as centre |
| 05:04 | and click again to get point 'B' |
| 05:10 | Let's draw an arc 'BC' |
| 05:13 | Click on "'Circular Arc with Center between Two points"' |
| 05:17 | Click on the point 'A', 'B' and 'C' on the circumference |
| 05:24 | An Arc 'BC' is drawn |
| 05:26 | Let's change the properties of arc 'BC' |
| 05:30 | In the "Algebra View" |
| 05:32 | Right click on the object 'd' |
| 05:35 | Select "Object Properties" |
| 05:37 | Select color as green, click on Close. |
| 05:46 | Click on new point tool, mark points 'D' and 'E' on the circumference of the circle. |
| 05:56 | let's subtend two angles from arc BC to points 'D' and 'E'. |
| 06:03 | Click on "Polygon" tool, |
| 06:05 | click on the points 'E', 'B', 'D', 'C' and 'E' again to complete the figure. |
| 06:18 | Let's measure the angles 'BDC' and 'BEC' |
| 06:26 | Click on the "Angle" tool, |
| 06:28 | Click on points 'B', 'D', 'C' and 'B', 'E', 'C' |
| 06:40 | We can see that the angles 'BDC' and 'BEC' are equal. |
| 06:51 | Let's state a next theorem |
| 06:55 | Angle subtended by an arc at the center, is twice the inscribed angles subtended by the same arc |
| 07:06 | Angle BAC subtended by arc BC at A is twice the inscribed angles BEC and BDC subtended by the same arc |
| 07:22 | Let's verify the theorem |
| 07:26 | Let's draw a sector 'ABC' |
| 07:30 | Click on the '"Circular Sector with Center between Two Points"' tool. |
| 07:35 | click on the points 'A', 'B', 'C' |
| 07:45 | Let's change the color of sector 'ABC'. |
| 07:48 | Right click on sector 'ABC' |
| 07:51 | Select "Object Properties". |
| 07:54 | Select Color as “Green”. Click on "Close". |
| 08:00 | Let's the measure angle 'BAC' |
| 08:04 | Click on the "Angle" tool , Click on the points 'B', 'A', 'C' |
| 08:15 | Angle 'BAC' is twice the angles 'BEC' and 'BDC' |
| 08:28 | Let's move the point 'C' |
| 08:32 | Notice that angle 'BAC' is always twice the angles 'BEC' and 'BDC' |
| 08:41 | hence theorems are verified |
| 08:45 | With this we come to the end of this tutorial |
| 08:48 | let's summarize |
| 08:53 | In this tutorial, we have learnt to verify that: |
| 08:57 | * Perpendicular from center to a chord bisects it |
| 09:00 | * Inscribed angles subtended by the same arc are equal |
| 09:06 | * the Central angle of a circle is twice any inscribed angle subtended by the same arc |
| 09:15 | As an assignment I would like you to verify |
| 09:19 | Equal chords of a circle are equidistant from center. |
| 09:24 | Draw a circle. |
| 09:25 | Select Segment with Given length from point tool |
| 09:29 | Use it to draw two chords of equal size. |
| 09:33 | Draw perpendicular lines from center to chords. |
| 09:37 | Mark points of intersection. |
| 09:40 | Measure perpendicular distances. |
| 09:44 | Assignment output should look like this |
| 09:48 | Watch the video available at this url: http://spoken-tutorial.org/What is a Spoken Tutorial |
| 09:51 | It summarises the Spoken Tutorial project |
| 09:53 | If you do not have good bandwidth, you can download and watch it |
| 09:58 | The Spoken Tutorial Project Team : |
| 10:00 | Conducts workshops using spoken tutorials |
| 10:03 | Gives certificates to those who pass an online test |
| 10:06 | For more details, please write to contact@spoken-tutorial.org |
| 10:14 | Spoken Tutorial Project is a part of the Talk to a Teacher project |
| 10:18 | It is supported by the National Mission on Education through ICT, MHRD, Government of India |
| 10:25 | More information on this Mission is available at this link |
| 10:29 | This is Madhuri Ganapathi from IIT Bombay signing off .Thank you for joining |
